Visual perception, receiving a two-dimensional (2D) visual input, often constructs the three-dimensional (3D) perceptual image. Although there are generally multiple structures in the external world that give an equivalent two-dimensional retinal image, the perceptual process naturally and easily infers only one 3D structure as the solution. However, the following problems are not obvious at all: what kind of structure can be obtained as a 3D perceptual image from certain 2D information, and why do we get a three-dimensional perceptual image instead of a two-dimensional one. In the present study, we investigate this problem by untangling the Necker Cube phenomenon, and propose a novel theory of three-dimensional visual perception from the viewpoint of the efficiency of information coding. Among the possible structures that can yield the 2D retinal image of the Necker Cube, the structure of the typical three-dimensional perceptual image of the Necker Cube maximizes the symmetry (in group theory). This maximization of symmetry is characterized by the pairs of adjoint functors (in category theory). Therefore, according to this proposed theory, “the Necker Cube” in the three-dimensional space is perceived as the most efficient encoding of the two-dimensional retinal image.
